Restoration of chiral symmetry in the large-N_c limit

TL;DR

This paper investigates how the critical temperature for chiral symmetry restoration scales with N_c in different models, revealing that modifications to the sigma-model can align its behavior with the NJL model.

Contribution

It demonstrates that incorporating temperature-dependent parameters and Polyakov loop coupling in the sigma-model changes its N_c scaling to match the NJL model.

Findings

NJL model predicts T_c independent of N_c

Original sigma-model predicts T_c proportional to N_c^{1/2}

Modified sigma-model with improvements predicts T_c independent of N_c

Abstract

We study the large-N_c behavior of the critical temperature T_c for chiral symmetry restoration in the framework of the Nambu-Jona-Lasinio (NJL) model and the linear \sigma-model. While in the NJL case T_c scales as N_c^0 and is, as expected, of the same order as \Lambda_QCD (just as the deconfinement phase transition), in the \sigma-model the scaling behavior reads T_c \propto N_c^1/2. We investigate the origin of the different scaling behavior and present two improvements of the \sigma-model: (i) a simple, phenomenologically motivated temperature dependence of the parameters and (ii) the coupling to the Polyakov loop. Both approaches lead to the scaling T_c \propto N_c^0.